Download Magnetic Force on a Current

Chapter 20
Magnetic Fields and Forces
Review
 Magnetic fields
 Are due to moving charges

Right-hand rule 1
 Act similar to electric fields with important differences



Field lines make loops from north to south poles
No magnetic mono-poles
Force is perpendicular to direction of field
 Exert a force on moving charges

Right-hand rule 2
Right-Hand Rule
 Right-hand Rule 1 gives
direction of Magnetic
Field due to current
 Right-hand Rule 2 gives
direction of Force on a
moving positive charge
Section 20.1
Right-hand Rule 1
1
 What is the direction of
the magnetic field in
regions 1, 2 and 3?
 B1 and B3 are non-zero
I
2
 They would be zero if
these were two sheets
of current
I
3
Right-hand Rule 1
Right-hand Rule 2
 What is the direction of the
force on a charge moving
perpendicular to an external
magnetic field?
 What is the radius of the circle
formed by the charge’s
trajectory?
Section 20.3
Mass Spectrometer
 Uses magnetic forces to
separate particles by mass
and charge
 Ions with different masses will
travel in arcs with different radii
 Used to find the composition
of a material
 Calculate charge to mass ratio
Section 20.6
Example: Bubble Chamber
 Used in particle physics to
investigate decay products
 What is the sign of the
charge?
 What is the relative mass?
Hall Effect
 (+) charge moving to the
right and (-) charge
moving to the left produce
the same current direction
 The Hall Effect can
distinguish between the
two options
Section 20.6
Hall Effect, cont.
 For a current carrying wire in a perpendicular magnetic field, net
charge will accumulate on the top and bottom of the wire
 Measuring the potential difference between top and bottom will indicate
the sign of the charge carriers
Section 20.6
Example: Hall Effect
Side View
 What is the magnitude
I
V
and direction of the
magnetic field?
 ncopper = 8.47 x 1028 m-3
Front View
d
Magnetic Force on a Current
 An electric current is a collection of
moving charges
 Obeys magnetic force law
 From the equation of the force on a
moving charge, the force on a currentcarrying wire is
 The direction of the force is given by the
right-hand rule 2
Section 20.4
Ampère’s Law
 Ampère’s Law can be
used to calculate the
magnetic field when there
is symmetry
 Similar to Gauss’ Law for
electric fields
 Relates the magnetic field
along a path to the electric
current enclosed by the
path
Section 20.7
Ampère’s Law, cont.
 The magnetic field along a
closed path is related to the
current enclosed by that path
 μo is the permeability of free
space
 μo = 4 π x 10-7 T . m / A
 If B varies in magnitude or
direction along the path,
Ampère’s Law is not useful
Section 20.7
Magnetic Field of a Long Straight Wire
 Ampère’s Law can be used to
find the magnetic field near a
long, straight wire
 Choose a circular, closed path
 B|| is the same all along the path
 If the circular path has a radius
r, then the total path length is 2
πr
 Applying Ampère’s Law gives
μo I
B
2π r
Section 20.7
Example: Two Parallel Wires
 What is the force on
I
1
wire 1 due to wire 2?
 Is the force attractive or
r
L
repulsive?
2
 (Demonstration)
I
Field from a Current Loop
 It is not possible to find
a simple path along
which the magnetic field
is constant
 Ampère’s Law cannot be
easily applied
 From other techniques,
μo I
B
2R
Section 20.7
Field Inside a Solenoid
 By stacking many loops close
together, the field along the
axis is much larger than for a
single loop
 A helical winding of wire is
called a solenoid
 More practical than stacking
single loops
 For a long solenoid, there is
practically no field outside
Section 20.7
Example: Long Solenoid
What is the magnetic
field, B, inside a “long”
solenoid?
Torque on a Current Loop
 A magnetic field can produce a torque on a current loop
 Assume a square loop with sides of length L carrying a
current I in a constant magnetic field
 The directions of the forces can be found from right-hand
rule 2
Section 20.5
Torque, cont.
 On two sides, the current is parallel or antiparallel to the field, so the
force is zero on those sides
 The forces on sides 1 and 3 are in opposite directions and produce a
torque on the loop
 When the angle between the loop and the field is θ, the torque is
τ = I L2 B sin θ
 For different shapes, this becomes
Section 20.5
τ = I A B sin θ
Magnetic Moment, μ
 For a current loop, the
magnetic moment, μ, is I A
 The direction of the magnetic
moment is either along the axis
of the bar magnet or
perpendicular to the current
loop
 The strength of the torque
depends on the magnitude of
the magnetic moment
 τ = μ B sin θ
Section 20.5
Electric Motor
 A magnetic field can produce a torque on a current loop
 If the loop is attached to a rotating shaft, an electric motor
is formed
 In a practical motor, a solenoid is used instead of a single
loop
 Additional set-up is needed to keep the shaft rotating
Section 20.10
Electric Generator
 Electric generators are closely related to motors
 A generator produces an electric current by rotating
a coil between the poles of the magnet
 A motor in reverse
Section 20.10